Ellipsoidal Harmonics
eBook - PDF

Ellipsoidal Harmonics

Theory and Applications

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Ellipsoidal Harmonics

Theory and Applications

Book details
Table of contents
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About This Book

The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.

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Yes, you can access Ellipsoidal Harmonics by George Dassios in PDF and/or ePUB format, as well as other popular books in Mathematik & Mathematik Allgemein. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2012
ISBN
9781139511841
Topic
Mathematik
Subtopic
Mathematik Allgemein

Table of contents

  1. Cover
  2. ELLIPSOIDAL HARMONICS: Theory and Applications
  3. Title
  4. Copyright
  5. Contents
  6. Prologue
  7. 1 The ellipsoidal system and its geometry
  8. 2 Differential operators in ellipsoidal geometry
  9. 3 Lamé functions
  10. 4 Ellipsoidal harmonics
  11. 5 The theory of Niven and Cartesian harmonics
  12. 6 Integration techniques
  13. 7 Boundary value problems in ellipsoidal geometry
  14. 8 Connection between sphero-conal and ellipsoidal harmonics
  15. 9 The elliptic functions approach
  16. 10 Ellipsoidal biharmonic functions
  17. 11 Vector ellipsoidal harmonics
  18. 12 Applications to geometry
  19. 13 Applications to physics
  20. 14 Applications to low-frequency scattering theory
  21. 15 Applications to bioscience
  22. 16 Applications to inverse problems
  23. Epilogue
  24. Appendix A: Background material
  25. Appendix B: Elements of dyadic analysis
  26. Appendix C: Legendre functions and spherical harmonics
  27. Appendix D: The fundamental polyadic integral
  28. Appendix E: Forms of the Lamé equation
  29. Appendix F: Table of formulae
  30. Appendix G: Miscellaneous relations
  31. Bibliography
  32. Index